PART 1) Two different balls are rolled (without slipping) toward a common finish

Question

PART 1) Two different balls are rolled (without slipping) toward a common finish line. Their angular speeds are 21.2 rad/s (Ball 1) and 15.8 rad/s (ball 2). The first ball, which has a radius of 0.0688 m, is rolling along a conveyor belt which is moving at 2.19 m/s and starts out 9.17 m from the finish line. The second ball has a radius of 0.0428 m and is rolling along the stationary floor. If the second ball starts out 5.99 m from the finish line, how long does each ball take to reach the finish line?

PART 2) What angular speed would the losing ball have needed to cross the finish line at the same time as the winning ball?

Explanation / Answer

Towards the two speeds add and become relative speed
W = V + U = WR + 2.19
= 21.2*.0688 + 2.19 = 3.64856 m/s = 3.65 m/s
So t = S/W = 9.17/3.65 = 2.51 seconds to the finish line.

Away W = V - U = ? and T = S/W = ? you can do the work.

Ball two W = v + 0 = wr = 15.8*.0428 = ? m/s
and T = D/wr = 5.99/(15.8*.0428) = 8.86 seconds.
This one will come in a poor second if they both start at the same time and given distances.

Ball two needs w = D/tr = 5.99/(2.51*.0428) = 55.76 rad/s

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